In order to analyze a geological structure of a subterranean formation, exploration geophysicists make many assumptions. One of them is that the subterranean formation is isotropic while in fact it is fundamentally anisotropic. This faulty assumption may result in erroneous imaging and interpretation of the geological structure. To extend the seismic processing techniques to anisotropic media, it is desirable to obtain a measure of the anisotropy of the geological structure.
Seismic anisotropy can be defined as the dependence of seismic velocity on the direction of wave propagation. It is known that a transverse isotropy with tilted axis earth model or TTI earth model can be used to model the propagation of waves and obtain an image of the subterranean formation in anisotropic media. The physical parameters to describe a TTI earth model include (1) the symmetry axis, (2) P-wave (compressional) velocity along symmetry axis—Vp0, (3) a parameter that specifies how the velocities vary for small angles from the symmetry axis—δ, and (4) a parameter that determines the velocity at large angles from the axis of symmetry—η□ (See Thomsen, “Weak Elastic Anisotropy”, Geophysics. vol. 51, no. 10, October 1986 and Alkhalifah and Tsvankin, “Velocity analysis for transversely isotropic Media”, Geophysics, vol. 60, 1550-1566, 1995).
Some TTI earth models also use anisotropic parameter ε to describe the propagation of waves in an anisotropic medium. Parameter ε satisfies the following relationship η=(ε−δ)/(1+2δ). S (shear) wave velocity is required to completely describe a TTI earth model, but in P-wave processing, S-wave velocity is usually obtained using an empirical relationship with P-wave velocity.
Usually a TTI earth model is a three directional model. Each point in the model is described by its coordinates and the values of anisotropic parameters. In certain situations, only a few quantities of anisotropic parameters may be needed to fully define a model if the properties of the anisotropic medium do not change from point to point. However, in most situations, the TTI earth model requires a large number of spatially varying values of anisotropic parameters to accurately define the model.
The anisotropic parameters of a TTI earth model may be directly measured from core data. However, drilling a well and coring are very expensive processes and direct measurements are only possible at very few well locations. For 3D imaging, it is desirable to determine the anisotropic parameters of the TTI earth model using also laterally extended data.